THE VISIBLE STARS. 





To persons not familiar with optical researches it may appear incomprehen- 

 ( sible that a star presenting, even with the telescope, no' disk of sensible mag- 

 nitude, could, nevertheless, appear so splendid. There is, however, a law of 

 light, clearly established in optics, which will probably remove this difficulty. 

 It is demonstrated that the apparent brightness of an object is not diminished 

 by its removal from the eye, although tb* quantity cf light which it p\. 

 I decreased in a high proportion. This statement may appear at first paradoxi- 

 i cal ; let us, however explain it. 



j If the sun, for example, were removed to twice its present distance it would 

 , appear to the eye with half its present diameter ; yet, in its diminished size, 

 j t'he apparent brightness of its surface would be the same as that with which 

 j we behold it at the lesser distance. To illustrate this, let us suppose that a 

 small circular opening is made in a card, and that the card is presented to the 

 sun, so that a portion of the sun's disk only shall be seen through it, but that 

 that portion shall be circular ; the opening will present to the eye the appear- 

 ance of a sun of less magnitude than the real one, but of equal brightness. Let 

 j the card then be held at such a distance from the eye that the circular portion 

 I of the sun's disk visible through it shall have a diameter equal to half of the 

 f entire disk. A sun will thus be seen of equal brightness with the true sun, 

 ; but of only half the linear diameter, and one fourth the superficial magnitude. 



From this illustration it will be easily perceived that one object may be 

 i smaller than another in apparent magnitude, and that it may give less light, 

 . but, nevertheless, be equally bright. 



This being clearly understood, it remains to be shown, that if the sun were 

 j removed to double its present distance it would exhibit a surface to the eye as 

 ; bright, though only half of the diameter. To comprehend this, let it be re- 

 1 membered that the light which proceeds from the smaller sun seen from double 



> the distance, issues from the entire surface of the sun, while the light which 

 | would proceed from an equal portion of the sun's disk seen at its present dis- 

 i tance, would only proceed from one fourth of the entire area of the disk. The 

 ] actual quantity of light, therefore, which issues from the small sun, seen from the 

 / larger distance, is greater, in the proportion of 4 to 1, than that which proceeds 

 ! from the small portion of the larger sun, seen at the lesser distance. It fol- 

 i lows, then, that the actual quantity of light by which the object is rendered visi- 

 | ble at the greater distance, is four times more than that by which the equivalent 



> part of the nearer object is rendered visible at the lesser distance ; but in con- 

 J sequence of the distance being less in the latter case, the intensity of the les- 

 ) ser quantity of light is four times greater. In short, it follows that as the ob- 

 l ject recedes from the eye the quantity of light which proceeds from a given por- 

 [ lion of the visual area is increased in the same proportion as the square of the 

 } distance, while the intensity of the light is diminished in exactly the same pro- 

 ) portion. What is, therefore, lost in intensity by increased distance, is gained 



in quantity ; and the effect is, that the splendor of the object is not changed by 

 distance, but only its apparent magnitude. 



The apparent diameter of the sun is very nearly 2,000 seconds of a degree. 

 If it were removed to 2,000 times its present distance it would present a diam- 

 eter of one second ; but it would appear as bright as a small portion of the 

 present disk would appear having an apparent diameter 2,000 times less than its 



me appearance of such portiuu wumu uc, ao uj uiigum^t v~ *.~.* e 

 tude, that which the sun would have at 2,000 times its present distance. 



Since, then, the brightness of the stars, in the proper sense of the term j 

 iohtness, is' not diminished by increased distance, we shall be the less sur- 



I 



